GIOU阅读笔记

Generalized Intersection over Union: A Metric and A Loss for Bounding Box Regression

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1 IOU为何不能作为损失函数

现在普遍优化坐标框的方法是采用4个坐标点与真实值的偏移的L1或者L2范式，上图表明，当它们具有相同的L1或者L2范式的时候，iou的值或giou的值相差巨大，也就是说优化坐标并不能直接优化iou值。那么为什么不直接用IOU作为损失函数？
因为当两个物体不重合的时候，它们的iou总是0，不管距离远近，梯度为0无法优化，所以无法作为损失函数。

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2 GIOU 定义如下：

GIOU作为损失函数：

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3 GIOU的性质：

1. Similar to IoU, GIoU as a distance, e.g. LGIoU =1-GIoU, holding all properties of a metric such as non-negativity, identity of indiscernibles, symmetry and triangle inequality.
2. Similar to IoU, GIoU is invariant to the scale of the problem.
3. GIoU is always a lower bound for IoU,and this lower bound becomes tighter when A and B have a stronger shapesimilarity and proximity.
4. 0 < IoU(A;B)<1, but GIoU has a symmetric range, -1 I) Similar to IoU, the value 1 occurs only when two objects overlay perfectly.
   II) GIoU value asymptotically converges to -1 when the ratio between occupying regions of
   two shapes,and the volume (area) of the enclosing shape tends to zero.

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4 实验